User talk:Emlightened
Surprisingly, this is a talk page. Feel free to ask about anything, and tell me if I screwed up editing something somewhere. Feedback about blog posts is welcome. Emlightened (talk) 02:45, January 1, 2016 (UTC) About BEAF I'd have to agree about BEAF, I think it's a little overrated. I think the reason most people like it is because it was one of the earlier notations and very ambitious for its time, but I really don't like how Bowers didn't even bother to explain how his system works after \(\zeta_0\) and left everybody guessing to this very day. I'm personally a lot more impressed by Saibian's work, he made it to \(\phi(\omega,0,0)\), being perfectly well defined every step of the way, and wrote some great introduction articles with useful guidelines as well as a giant book thing with something like 15000 number names. Pteriforever (talk) 06:35, January 1, 2016 (UTC) : It has the potential to be cool, but as it was left, it was vague, weak, and not well defined. Bird did better, as did Saibian, but I think I probably prefer Hollom, for the relatively small definition that still contains great power. Shame that there's not as much much analysis on the limit of his notation, though I'd guess it's either \(\theta(\varphi(\Omega,1))\) or \(\theta(\Gamma_{\Omega+1})\). Emlightened (talk) 22:45, January 1, 2016 (UTC) : For all of BEAF's weaknesses (and there are many) and it's overratedness (yes, I wrote that), I still think that it deserves some "respect". His linear and tetrational areays show an intuitive and fairly easy way of reaching up to w^w and e_0 respectively, and his way of thinking of separators as dimensions is a concept that inspired many others, Hollom and Saiban (well, Saiban from a different aspect, but I'm trying not to be nitpicky here). : BEAF was revolutionary, but wasn't perfect. I prefer not to see it as the height of googology (which is incorrect anyway, as many notations pass it), but as a stepping stone: a founder of modern googology. : Honestly though, I think most people like it because of Meameamealokkapoowa oompa ;) Maybe called Googology Noob (talk) 19:22, January 2, 2016 (UTC) : I can definitely see how a number like Meameamealokkapoowa oompa would help. And I've also not actually seen BEAF as inspiring before, although I guess it certainly is that. Dimensional arrays are certainly one of the most popular ways to get into \(\varepsilon_0\)-level ordinals now. Emlightened (talk) 10:50, January 3, 2016 (UTC) : To be fair, BEAF is also a very elegant and intuitive outline for a notation which was - for its time - very strong. The array-of operator is ingenious, even though it wasn't really well-defined. PsiCubed2 (talk) 23:15, December 25, 2016 (UTC) Your ordinal notation I was just curious, how did it go with the ordinal notation that you were intending to publish? Is it still under a veil of secrecy? Deedlit11 (talk) 13:56, December 25, 2016 (UTC) : Hehe. I don't know if I ever will end up using it, but I hope so (it seems to allow a much more general and precise version of the inaccessible notations etc. compared to those in Killing Them Softly p28-p29, for instance). My main roadblock is that I'm not what to write about it, or even how I could publish it or anysuch. I'm probably being a bit excessive with wanting to keep it secret etc., but my Granddad once told me that a patent him and a friend were working on got signed under just the friend's name behind his back, and that it could never be accredited to him. So meh, maybe academia is a cutthroat business. : In the end, I got it in two forms. One of them used a standard ordinal-notation framework, but doesn't seem like it can be generalised to something with arbitrarily large parameters or something like the lower-down functions. The other method argued outside of the universe, so wasn't natural. Besides all of that, as most of my knowledge of set theory has been formed by reading on the internet, I actually have no idea how to string a proof together, which kinda sucks. I haven't managed to prove them equivalent yet, but I wouldn't know where to start anyway. ~εmli 23:00, December 25, 2016 (UTC) I think the best way to insure that you get credit is actually to publish your work in a manner that makes it clear that you are the author, with the date clearly established. I don't think academia is as cutthroat as you fear in regards to stealing other's work, plagiarism is taken very seriously. I think you could even just write up your work on your Google Sites page, if you have your name on it somewhere. Otherwise, putting it up on ArXiV would be nice if you could get someone to vouch for you, but just something like Google Docs should work as well. Deedlit11 (talk) 08:37, January 17, 2017 (UTC) Big Bigeddon You mentioned how Little Bigeddon is the smaller of the two. I'm guessing, therefore, that it is called "Big Bigeddon". Out of interest, have you finished this larger Biggeddon, or have you not really started? Just interested, since I'm wondering when your numbers will be published on the mainspace :P : Not started it yet, actually. I've got a basic outline for what I want to make, but I've only just sorted out the last of the more technical details. As far as the mainspace goes, there's a link to a source in the bottom-left corner of my homepage that has pretty much just a copied version of that blog post in it. ~εmli 20:22, January 15, 2017 (UTC) : Edit: Okay, maybe not. I should try assuming V=HOD next, and see if I can work it out later. 07:13, January 16, 2017 (UTC) ::Can I make a suggestion? Since you're on Google Sites, MathJax won't run. You could use GitHub pages like so: https://mush9.github.io/googology/0/little-bigeddon.html (and I'll be happy to host it for you :P) Mush9 (talk) 08:39, January 16, 2017 (UTC) :::Thanks for the suggestion! If you do want to host it, then I'm happy to let you (but can I ask that you link the GSites page as well?) ~εmli 17:56, January 16, 2017 (UTC) ::::Sure - I'm going to make an article on the mainspace about Little Bigeddon and include both links and a link from GHPages to GSites. Mush9 (talk) 18:04, January 16, 2017 (UTC) :::: Edit: http://googology.wikia.com/wiki/Little_Bigeddon Tada! ::::: Thank you, and squeee! I'll see how I can add to it later. ~εmli 22:50, January 18, 2017 (UTC) ::If you doing mind me asking once again: How's progress with Big Bigeddon? I'm really intrigued :P Mush9 (talk) 19:47, February 5, 2017 (UTC) NBG* in ZFC Since you've said elsewhere you don't tend to check old(ish) blog posts, I'm writing here to ask you to take a look at this comment I've made, since I'm really curious about the answer. LittlePeng9 (talk) 11:45, January 22, 2017 (UTC) Favorite number What's your favorite number? :D If you have one?Itti (talk) 16:45, January 30, 2017 (UTC)Itti Math Symbols I noticed on your profile page you have a description of a cardinal hierarchy, but you seemed to be having trouble with representing the symbols on the page. So here it is, if you want to copy and paste it in. \mathbf{Card} is the class of cardinals and \mathbf{Reg} is the class of uncountable regular cardinals - \text{M} is the least weakly Mahlo cardinal, and \mathbf{I_{Card}} is the class of weakly inaccessible cardinals. For \nu\neq\text{M} : C_0(\nu,\alpha)=B(\nu)\cup M C_{n+1}(\nu,\alpha)=\{\beta+\gamma|\beta\and\gamma\in C_n(\nu,\alpha)\}\cup\{\psi_{\beta}(\gamma)|\beta\and\gamma\in C_n(\nu,\alpha)\and(\gamma<(\alpha\or\beta)=M)\} C(\nu,\alpha)=\cup\{C_n(\nu,\alpha)|n<\omega\} \psi_{\nu}(\alpha)=\min(D(v)\setminus C(\nu,\alpha)) For \nu=\text{m} : \psi_M has to be done completely differently to diagonalize across the inaccessibles. Try making normal \chi and associated sets and have \psi_M be a one-variable version ? (Straight diagonal, \vartheta like), or increasing diagonal \psi -like ?) B_0(\alpha,\beta)=\beta\cup\{0,M\} B_{n+1}(\alpha,\beta)=\{\gamma+\delta,\omega^{\gamma},\chi_{\nu}(\gamma)|\gamma,n<\omega\} \chi_{\alpha}=\text{enum cl }\{\pi|\beta(\alpha,\pi)\cup M=\pi\and\alpha\in B(\alpha,\pi)\} D'(0)=M D'(1+\alpha)=\{\chi_{\alpha}(\beta)|\beta D(\alpha)=D'(\max\{\delta|\exists\gamma(\alpha=\gamma\cdot M^{\delta})\}) B(0)=1 B(\gamma\cdot M^{\delta})=\omega_{\gamma\cdot M+\delta}\text{ where }0<\delta B(\gamma\cdot M^{\delta})=...(0<\delta) C_0(\alpha)=\{0\} C_{n+1}(\alpha)=\{\gamma+\delta\text{, }\omega^{\Omega+\gamma}\text{, }\psi(\mu)|(\gamma\and\delta\and\mu)\in C_n(\alpha)\and(\mu<\alpha)\} C(\alpha)=\cup\{C_n(\alpha)|n<\omega\} \psi(\alpha)=\min(\Omega\setminus C(\alpha)) \alpha=_{NF}\gamma+\delta\Leftrightarrow\alpha=\gamma+\delta\and 0<\delta<\gamma\cdot\omega\and(\forall\delta<\beta)(\delta+\beta=\beta) \alpha=_\text{NF}\omega^{\Omega+\gamma}\Leftrightarrow\alpha=\omega^{\Omega+\gamma} \alpha=_\text{NF}\psi(\gamma)\Leftrightarrow\alpha=\psi(\gamma)\wedge\alpha\not=\psi(\gamma+1) \alpha=_\text{NF}\gamma+\delta\Rightarrow\alphan=\gamma+\deltan \alpha=_\text{NF}\omega^{\Omega+\gamma}\wedge\text{cof }\gamma=0\Rightarrow\alpha\beta=\beta \alpha=_\text{NF}\omega^{\Omega+\gamma}\wedge\text{cof }\gamma=1\Rightarrow\alphan=\omega^{\Omega+\gamma0}n \alpha=_\text{NF}\omega^{\Omega+\gamma}\wedge\text{cof }\gamma>1\Rightarrow\alphan=\omega^{\Omega+\gamman} \alpha=_\text{NF}\psi(\gamma)\wedge\text{cof }\gamma=0\Rightarrow\alpha0=0 \alpha=_\text{NF}\psi(\gamma)\wedge\text{cof }\gamma=1\Rightarrow\alphan=\psi(\gamma0)n \alpha=_\text{NF}\psi(\gamma)\wedge\text{cof }\gamma=\omega\Rightarrow\alphan=\psi(\gamman]) \alpha=_\text{NF}\psi(\gamma)\wedge\text{cof }\gamma=1\Rightarrow\alphan= (\beta\mapsto\psi(\gamma\beta))^n(0) Edwin Shade (talk) 04:00, November 22, 2017 (UTC) Discord Hey! Me and the rest in the NEOS server wish to invite you there! If you have a Discord account, please message me. Thanks! Boboris02 (talk) 16:49, March 4, 2018 (UTC) Compliment by Meowzz ur work is inspiring (: